A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must contain 5,000 square meters in order to provide enough grass

Question

A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must contain 5,000 square meters in order to provide enough grass for the herd. No fencing is needed along the river. What dimensions will require the least amount of fencing?

Answer 1

A = LW = 5,000

L=5,000/W

Perimeter = P = L +2W = 5,000/W +2W

P' = 2 -500/W^2 = 0

multiply by W^2 to get

2W^2 -500 =0

W^2 = 500/2 = 250

W = sqr250 = 5sqr10 meters = width

L = 500/5sqr10 = 100/sqr10 = 100sqr10/10 = 10sqr10 meters = length paralelel to the river

dimensions are 5sq10 by 10sqr10

= about slightly more than 15.8 by slightly more than 31.6 meters

Area - 5sqr10(10sqr10) = 500 m^2

15.8 x 31.6 = 499.28